Abstract

This paper is an extension of results established by Jauch and Misra [Helv. Physica Acta 38, 30 (1965)] concerning finite or countable sets of commuting self‐adjoint operators. We have obtained the following results: let A={Ai}i‐I be a set of commuting self‐adjoint operators on a separable Hilbert spaceH. Then (i) for any I (possibly noncountable), there exists a spectral representation for A iff A″ is maximal Abelian. (ii) If I is finite or countable, ‐i‐I,n‐ND (Ani) is dense in H. As a corollary of a theorem of Maurin [Bull. Acad. Pol. Sci., Sér. Sci. Math. Astron. Phys. 7, 471 (1959)], this implies the existence of a common complete set of generalized eigenvectors.